Question

If a confidence interval has a width of 1 point based on a sample of 50 observations, what is the width if the sample size is increased to 800 (assuming everything else remains constant)?

a) Less than 1 point
b) Exactly 1 point
c) More than 1 point
d) Cannot be determined from the information provided

Answer 1

If the sample size is increased from 50 to 800, the width of the confidence interval will be more than 1 point.

Step-by-step explanation:

The width of a confidence interval can be calculated using the formula:

Width = 2 * (critical value) * (standard deviation / square root of sample size)

Since everything else remains constant, the critical value and standard deviation will not change. Thus, the width of the confidence interval will only depend on the square root of the sample size. Therefore, if the sample size is increased from 50 to 800, the width of the confidence interval will be:

Width' = Width * sqrt(800/50) = Width * sqrt(16) = Width * 4

So, the new width will be 4 times the original width, which means the width will be more than 1 point.